On an absolutely up-to-date Mint13 here, there is a file named /etc/os-release. It has been introduced by some Ubuntu update which turned the underlying Ubuntu into 12.04.2. The content of the file /etc/os-release reads

It returns the string precise here.Provided the same file /etc/os-release exists on Nadia as well, the command should return quantal in your case.I cannot check right now because I am on Mint 13. But I will definitely check next time I boot up Nadia.

On Olivia, the previous solution doesn't work for me(Ubuntu version : 13.04, Raring Ringtail)so to install JOSM with the openstreetmap.de repository andstay with a recent version of this amazing tool you can use these commands :